Calculus I - Spring 2008


Instructor: S. M. Mintchev

Meeting Times: Mon 9:00am-11:00am; Th 12:00pm-1:00pm; F 2:00pm-4:00pm

Locations: Mon - Rm. 521; Th - Rm. 315; Fri - Rm. 143

Instructor Information:

General Information about the Course: This course is the first in the Calculus sequence taught at Cooper Union. We will introduce the concepts of limits, continuity, differentiation, and Riemann integration to the study of real-valued functions of one variable. The goal for the course is to introduce students to some important applications of calculus to the physical sciences. Mastery of computational techniques, as well as a developed sense for mathematical formulation of scientific problems will be expected.

Text: Calculus and Analytic Geometry. Stein, Sherman K. and Barcellos, Anthony. Fifth edition. McGraw-Hill, 1992.

Grading Policy: There will be six homework assignments collected throughout the semester. This page will contain a posting of required and suggested homework exercises from each section covered. Required problems are marked with an asterisk. In addition to these assigments there will be two exams during the semester; the exams will be administered at the one third, resp. two thirds, marks of the semester. The first exam will cover the first third of the material; the second will cover the second third. There will be a final examination administered on the last day of class; this exam will cover all of the material taught in the course. The values of these components towards the final grade in the course are presented below:

Component
 Value
Homework
 20 %
Exam 1
 25 %
Exam 2
 25 %
Final Exam
 30 %

Syllabus (please note that this schedule is tentative and will likely be adjusted as the semester progresses):

Date
 Chapter.Section
 Topic
01/24/2008
 I
 Introduction and Notation, Course Information
01/25/2008 2.1, 2.2 Review of Real Number System and Functions
01/28/2008 2.3, 2.4, 2.10
 Definition of Limit, Computations
01/31/2008 2.4, 2.8, 2.9
 Continuity, More Computations of Limits
02/01/2008 2.6, 2.7
 Trigonometric Limits
02/04/2008 3.1, 3.2
 The Derivative
02/07/2008 3.3, 3.4
 Derivative & Continuity; Rules For Differentiation
02/08/2008 3.5, 3.6
 Derivatives of Trigonometric Functions; Chain Rule
Homework 1 DUE
02/11/2008 4.1, 4.2
 Rolle's Theorem & Mean-Value Theorem; Graphing
02/14/2008 4.3
 Second Derivative; Kinematics
02/15/2008 4.4, 4.5
 Related Rates; Graphing
02/21/2008 4.6,
 Newton's Method;
02/22/2008 4.7, 4.8
 Optimization; Implicit Differentiation;
02/25/2008 4.9, 4.10
 Linear Approximation; Growth Estimates
Homework 2 DUE
02/28/2008 REVIEW
 Review for Exam 1
02/29/2008 EXAM 1
 Sections 2.1-4.8
03/03/2008 Graphing Workshop
 A Review of Graphing Tools; Examples
03/06/2008 Exam 1; 5.1
 Area Estimates
03/07/2008 5.2-5.4
 Summation Notation, Definite Integral, Estimations
03/10/2008 5.5,5.6
 Antiderivatives, Intro to Fundamental Theorem
03/13/2008 5.7
 Fundamental Theorem of Calculus
03/14/2008 6.1,6.2
 The Logarithm and Natural Number e
Homework 3 + Graphing Worksheet DUE
03/24/2008 6.3,6.4
 Derivatives of Logarithmic Functions
03/27/2008 6.5
 Derivatives of Exponential Functions
03/28/2008 6.6,6.7
 Derivatives of Inverse Trig, Natural Growth/Decay
03/31/2008 6.8,6.9
 L'Hopital's Rule; Hyperbolic Functions
04/03/2008 REVIEW
 Review for Exam 2
04/04/2008 EXAM 2
 Sections 4.9-6.7; Graphing
Homework 4 DUE
04/07/2008 Workshop: 7.1
 Integration with Integral Tables
04/10/2008 Workshop: 7.2 Integration by Substitution
04/11/2008 Workshop: 7.3 Integration by Parts
04/14/2008 Workshop
 Special Techniques for Integrals of Trig Functions
04/17/2008 Workshop: 7.4 Integration of Rational Functions
04/18/2008 Workshop: 7.5 Method of Partial Fractions
04/21/2008 Workshop: Some Special Methods: Rational fns. of sine and cosine
04/24/2008 Workshop: 7.6 Special Substitutions
04/25/2008 Workshop: 7.7 Work on Integration (students at Blackboard)
Homework 5 DUE
04/28/2008 Workshop Final Review Exercises (students at Blackboard)
05/01/2008 Workshop Final Review Exercises (students at Blackboard)
05/02/2008 Workshop Final Review Exercises (students at Blackboard)
05/05/2008 Workshop Final Review Exercises (students at Blackboard)
05/08/2008 Workshop Final Review Exercises (students at Blackboard)
05/09/2008 Workshop Final Review Exercises (students at Blackboard)
Homework 6 DUE
05/12/2008 FINAL EXAM
 Cumulative (covers entire course)

Homework Assigments (please see grading policy section for requirements):

* - submission of problem required for grading

Section
 Problem
2.1 17,21*,22,23,27*,28*,41,44,(46-53)*
2.2
 19,22,24,26,29*,30*,31,32*,33,34,35,36*
2.3
 2*,4,6*,8,10,12*,13*,14*,16,20,22*,27,28,29,30*
2.4
 4,10,17*,20,22*,33*,39*,46*
2.5
 3,4,5*,29-31,32*,35*,36*,41*,42,43,44
2.6
 43*,51,52*,53*,54*,56
2.7
 (3-10)*,15,16*,28*
2.8
 1-10,12*,16*,26*,37,39*,40*
3.1
 6*,9,18*
3.2
 11,14,16, 25*, 28*, 38*, 40*
3.3
 1, 3, 9, (15-18)*, (26-28)*
3.4
 14, 18*, 24, 28, 34*, 35*, 38*, (47-48)*
3.5
 19-21, (22-24)*, 34*, 44*
3.6
 19*, 20*, (28-30)*, 37*, 38*, 54*
4.1
 8, 10*, 18*, 26*, 46*
4.2
 8*, (9-16)*, 44, 48*
4.3
 23, 26, 28*
4.4
 4, 5, 10, 17*, 23*
4.5
 11, 14, 16*, 24*, 25, 35*, 40*, 41
4.6
 19, 26, 28
4.7
 8*, 11, 12, 16, 25*, 30*, 37, 39, 46*, 50*
4.8
 3*, 20*
4.9
 9,10*,11,12*,12,14,15,16*,42*,46,49*
4.10
 16,17*
5.1
 7*,8*,30*
5.2
 12*,21*,28,34*
5.3
 4,7*,24,29*,32*
5.4
 21-26,30*
5.5
 12,17*,24,26*,39*
5.6
 10*,11,16*
5.7
 (5-16)*,39*,44*
6.1
 25*,26,28*,34*
6.2
 13*,16(c)*
6.3
 12,16,22*,37*,38*
6.4
 5,6,8*,21*
6.5
 9,13,14*,38*,40*
6.6
 15,18,20*,24,26*,31*,36*
6.7
 3*,4,7,8*,21*,39,40*
6.8
 2*,8,10*,12*,20*,33*,24,46,54*
6.9
 15,16,18*,22,34*,37
Ch .6 review
 6,8,14,30,41*,58,95,96*,109,118*,124*,145*
7.1 8*,9*,11*,15*
7.2 3*,8*,9*,14*,18*,31*,34*
7.3 2*,4*,12*,15*,16*,19*,33*,36*,37*
7.4 4*,11*,13*,16*,21*,24*,33*,36*
7.5 (3-8)*,20*,24*,26*,32*,49*,52*,58*
7.6 3*,7*,8*,14*,20*,24*,27*,42,43,49*,52,55*
7.7 1-59 (* - multiples of 4 are for credit)
Ch.7 review
 43-161 (* - multiples of 5 are for credit)